QNetDiff: a quantitative measurement of network rewiring

Bacteria in the human body, particularly in the large intestine, are known to be associated with various diseases. To identify disease-associated bacteria (markers), a typical method is to statistically compare the relative abundance of bacteria between healthy subjects and diseased patients. However, since bacteria do not necessarily cause diseases in isolation, it is also important to focus on the interactions and relationships among bacteria when examining their association with diseases. In fact, although there are common approaches to represent and analyze bacterial interaction relationships as networks, there are limited methods to find bacteria associated with diseases through network-driven analysis. In this paper, we focus on rewiring of the bacterial network and propose a new method for quantifying the rewiring. We then apply the proposed method to a group of colorectal cancer patients. We show that it can identify and detect bacteria that cannot be detected by conventional methods such as abundance comparison. Furthermore, the proposed method is implemented as a general-purpose tool and made available to the general public.


Step 2
Input: list of effective bacteria and its adjacency matrix output by Step 1 (bacteria effective, correlation effective X , correlation effective Y ).Output: list of representative bacteria (bacteria representative) and adjacency matrix of network after contraction (correlation representative X , correlation representative Y ).
Step 2.1 Input: list of effective bacteria and its adjacency matrix output by Step 1 (bacteria effective, correlation effective X , correlation effective Y ) Output: cluster number of effective bacteria (cluster X , cluster Y ).
Step 2.2 Input: list of effective bacteria output by Step 1 (bacteria effective) cluster number of effective bacteria (cluster X , cluster Y ), one level higher category of bacteria (sup category).Output: array of similar bacteria group within a cluster (similar groups in cluster).

Step 4
Input: array of core bacteria output by Step 3 (bacteria focused), array of representative bacteria and its adjacency matrix output by Step 2 (bacteria representative, correlation representative X and correlation representative Y ).Output: a pair of networks (G X , G Y ) consisting of core bacteria and related bacteria.

Step 5
Input: a pair of networks (G X , G Y ) consisting of core bacteria and related bacteria output by Step 4. Output: rewiring index (QNetDiff score) QNetDiff of core bacteria and related bacteria in G X and G Y .
Listing 5: Pseudo-code of Step 5.  1 and     2, we show information on the bacterial correlation network constructed from these genera before and after the unification (contraction) of bacteria.The contraction is performed for Healthy and each of the other four stages, and the results are shown below.We show in Supplementary Table 3 the list of genera groups unified as similar bacteria within a cluster by step 2 of the proposed method and the representative bacteria of each group.Also, Supplementary Table 4 shows a list of bacteria unified in a single genus.

Supplementary
Supplementary Table 3.A list of 32 unified groups of genera (32 groups) of two or more sizes, the size of each group, and the representative bacteria of each group.They contain 156 kinds of genera.
Input: array of similar bacteria groups within a cluster output byStep 2.2 (similar groups in cluster), relative abundance average of bacteria (abundance average).adjacencymatrix of effective bacteria output by Step 1 (correlation effective X , correlation effective Y ) Output: list of representative bacteria (bacteria representative)and adjacency matrix of network after contraction (correlation representative X , correlation representative Y ).
Basic Information on Data of Colorectal Cancer Patients used in the Experiments and the Bacterial Correlation NetworkAmong the 2,001 intestinal genera that appeared in the stool samples of 576 colorectal cancer patients used in this paper, there were 1,717 kinds that did not correlate with other genera in any of the following stages: Healthy, Multiple polyps, Stage 0, Stage I II, Stage III IV.Therefore, there are 284 genera that are correlated with other bacteria in one or more of the five stages.In the following Supplementary Tables

Table 1 .
Basic information on the bacterial correlation network before contraction at each stage.

Table 2 .
Information on the bacterial correlation network after unification of Healthy with each of the other four stages.Stage represents the two groups to be compared, and the unification is performed for the two groups.#nodes is the number of nodes having edges at any stage, and (#nodes having edges) is the number of nodes having edges at each stage.

Table 4 .
List of bacteria unified in a single genus.There are 92 kinds of genera belonging to this list.These are automatically representative bacteria.